5. Hypothetical Plants To compare logarithmic and exponen- tial growth, we consider two hypothetical plants species...
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5. Hypothetical Plants To compare logarithmic and exponen- tial growth, we consider two hypothetical plants species A and species B, but that exhibit rather different growth rates. The height of species A (measured in feet) at age t (measured in years) is given by L(t) = ln(t) + 1, 121 The height E (measured in feet) of species B at age t (measured in years), is given by E(t)=e-¹, 121 (a) Show that the plants have the same height at time t = 1. (b) Find the heights of each plant after 2, 10, 100 years. (c) How long does it take for each plant to double its height (i.e., grow to 2 feet tall)? (d) How long does it take to double height again (i.e., to reach 4 feet tall)? Compare with your answer to part (c). (e) How long does it take each plant to reach 3 feet tall? Com- pare to your answer to part (c). 5. Hypothetical Plants To compare logarithmic and exponen- tial growth, we consider two hypothetical plants species A and species B, but that exhibit rather different growth rates. The height of species A (measured in feet) at age t (measured in years) is given by L(t) = ln(t) + 1, 121 The height E (measured in feet) of species B at age t (measured in years), is given by E(t)=e-¹, 121 (a) Show that the plants have the same height at time t = 1. (b) Find the heights of each plant after 2, 10, 100 years. (c) How long does it take for each plant to double its height (i.e., grow to 2 feet tall)? (d) How long does it take to double height again (i.e., to reach 4 feet tall)? Compare with your answer to part (c). (e) How long does it take each plant to reach 3 feet tall? Com- pare to your answer to part (c).
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Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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